Improved Spectral Calculations for Discrete Schroedinger Operators

Date
2013-05
Journal Title
Journal ISSN
Volume Title
Publisher
Description
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/72024
Abstract

This work details an O(n^2) algorithm for computing spectra of discrete Schroedinger operators with periodic potentials. Spectra of these objects enhance our understanding of fundamental aperiodic physical systems and contain rich theoretical structure of interest to the mathematical community. Previous work on the Harper model led to an O(n^2) algorithm relying on properties not satisfied by other aperiodic operators. Physicists working with the Fibonacci Hamiltonian, a popular quasicrystal model, have instead used a problematic dynamical map approach or a sluggish O(n^3) procedure for their calculations. The algorithm presented in this work, a blend of well-established eigenvalue/vector algorithms, provides researchers with a more robust computational tool of general utility. Application to the Fibonacci Hamiltonian in the sparsely studied intermediate coupling regime reveals structure in canonical coverings of the spectrum that will prove useful in motivating conjectures regarding band combinatorics and fractal dimensions.

Description
This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/72024
Advisor
Degree
Type
Technical report
Keywords
Citation

Puelz, Charles. "Improved Spectral Calculations for Discrete Schroedinger Operators." (2013) https://hdl.handle.net/1911/102221.

Has part(s)
Forms part of
Published Version
Rights
Link to license
Citable link to this page